Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions
Abstract
Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the partition function on various manifolds and ground state degeneracy (GSD), mainly based on continuum/cochain topological quantum field theories (TQFTs), in any dimension. This information can be related to the counting of extended operators of bosonic/fermionic TQFTs. On the lattice scale, anyonic particles/strings live at the ends of line/surface operators. Certain systems in different dimensions are related to each other through dimensional reduction schemes, analogous to (de)categorification. Examples include spin TQFTs derived from gauging the interacting fermionic symmetry-protected topological states (with fermion $$\mathbb Z$$$$f\atop{2}$$) of parity symmetry groups $$\mathbb Z{_4}$$×$$\mathbb Z{_2}$$ and ($$\mathbb Z{_4}$$)2 in 3+1D, also $$\mathbb Z{_2}$$ and ($$\mathbb Z{_2}$$)2 in 2+1D. Gauging the last three cases begets non-Abelian spin TQFTs (fermionic topological order). We consider situations where a TQFT lives on (1) a closed spacetime or (2) a spacetime with a boundary, such that the bulk and boundary are fully gapped and short- or long-range entangled (SRE/LRE). Anyonic excitations can be deconfined on the boundary. We introduce new exotic topological interfaces on which neither particle nor string excitations alone condense, but only fuzzy-composite objects of extended operators can end (e.g., a string-like composite object formed by a set of particles can end on a special 2+1D boundary of 3+1D bulk). We explore the relations between group extension constructions and partially breaking constructions (e.g., 0-form/higher-form/“composite” breaking) of topological boundaries, after gauging. We comment on the implications of entanglement entropy for some such LRE systems.
- Authors:
-
- Institute for Advanced Study, Princeton, NJ (United States); Harvard Univ., Cambridge, MA (United States)
- Institute for Advanced Study, Princeton, NJ (United States)
- Princeton Univ., NJ (United States)
- Univ. of Science and Technology of China, Hefei (China)
- Harvard Univ., Cambridge, MA (United States)
- Harvard Univ., Cambridge, MA (United States); Tsinghua Univ., Beijing (China)
- Publication Date:
- Research Org.:
- Institute for Advanced Study, Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE; National Science Foundation (NSF); US–Israel Binational Science Foundation
- OSTI Identifier:
- 1499898
- Grant/Contract Number:
- SC0009988; PHY-1314311; 11431010; 11571329; PHY-1306313; PHY-0937443; DMS-1308244; DMS-0804454; DMS-1159412
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Progress of Theoretical and Experimental Physics
- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 5; Journal ID: ISSN 2050-3911
- Publisher:
- Physical Society of Japan
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Wang, Juven, Ohmori, Kantaro, Putrov, Pavel, Zheng, Yunqin, Wan, Zheyan, Guo, Meng, Lin, Hai, Gao, Peng, and Yau, Shing-Tung. Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions. United States: N. p., 2018.
Web. doi:10.1093/ptep/pty051.
Wang, Juven, Ohmori, Kantaro, Putrov, Pavel, Zheng, Yunqin, Wan, Zheyan, Guo, Meng, Lin, Hai, Gao, Peng, & Yau, Shing-Tung. Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions. United States. https://doi.org/10.1093/ptep/pty051
Wang, Juven, Ohmori, Kantaro, Putrov, Pavel, Zheng, Yunqin, Wan, Zheyan, Guo, Meng, Lin, Hai, Gao, Peng, and Yau, Shing-Tung. Wed .
"Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions". United States. https://doi.org/10.1093/ptep/pty051. https://www.osti.gov/servlets/purl/1499898.
@article{osti_1499898,
title = {Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions},
author = {Wang, Juven and Ohmori, Kantaro and Putrov, Pavel and Zheng, Yunqin and Wan, Zheyan and Guo, Meng and Lin, Hai and Gao, Peng and Yau, Shing-Tung},
abstractNote = {Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the partition function on various manifolds and ground state degeneracy (GSD), mainly based on continuum/cochain topological quantum field theories (TQFTs), in any dimension. This information can be related to the counting of extended operators of bosonic/fermionic TQFTs. On the lattice scale, anyonic particles/strings live at the ends of line/surface operators. Certain systems in different dimensions are related to each other through dimensional reduction schemes, analogous to (de)categorification. Examples include spin TQFTs derived from gauging the interacting fermionic symmetry-protected topological states (with fermion $\mathbb Z$$f\atop{2}$) of parity symmetry groups $\mathbb Z{_4}$×$\mathbb Z{_2}$ and ($\mathbb Z{_4}$)2 in 3+1D, also $\mathbb Z{_2}$ and ($\mathbb Z{_2}$)2 in 2+1D. Gauging the last three cases begets non-Abelian spin TQFTs (fermionic topological order). We consider situations where a TQFT lives on (1) a closed spacetime or (2) a spacetime with a boundary, such that the bulk and boundary are fully gapped and short- or long-range entangled (SRE/LRE). Anyonic excitations can be deconfined on the boundary. We introduce new exotic topological interfaces on which neither particle nor string excitations alone condense, but only fuzzy-composite objects of extended operators can end (e.g., a string-like composite object formed by a set of particles can end on a special 2+1D boundary of 3+1D bulk). We explore the relations between group extension constructions and partially breaking constructions (e.g., 0-form/higher-form/“composite” breaking) of topological boundaries, after gauging. We comment on the implications of entanglement entropy for some such LRE systems.},
doi = {10.1093/ptep/pty051},
journal = {Progress of Theoretical and Experimental Physics},
number = 5,
volume = 2018,
place = {United States},
year = {Wed May 30 00:00:00 EDT 2018},
month = {Wed May 30 00:00:00 EDT 2018}
}
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